Conjecture 1
Word and Meaning Minimum
1
Word is expressed by arbitrary figure W in space Rn.
Meaning minimum is expressed by n-dimensional sphere M that has diameter below δ.
W is covered by sequence of M.1, M2, M3, ….
Lower limit of all the covering ∑k (diam ( Mk ) ) α is expressed by Hα,δ ( W ).
Hα,δ ( W ) = inf diam ( Mk ) <δ (diam ( Mk ) ) α
2
Hα ( W ) : = limδ →0 Hα,δ ( W )
3
Word has non-positive real number or ∞ by Hα ( W ).
Hα ( W ) is restricted by measurable sets.
Hα ( W ) is treated as Hausdorff measure.
4
Word is expressed by Hausdorff measure.
Meaning minimum is expressed by limδ →0 M .
5
Word has α dimension.
Meaning minimum has n dimension.
6
Language consists of word and meaning minimum.
7
Language has dimension.
[References]
<On meaning minimum>
<On place of meaning>
<On confirmation of meaning>
Tokyo September 22, 2008
[Reference December 22, 2008]
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